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Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Age 14 to 16
Challenge Level
The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.
What is the area of a regular hexagon inscribed in a circle with a unit radius?
What is the area of an equilateral triangle inscribed in a circle with a unit radius?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.